I'm all for not making broad, far-reaching claims based on a controlled lab test or just a few observations. But both of the following two claims are ridiculous:

1. There is still disagreement on the physical reality of a simul-climbing fall, and because it is so complicated with so many potential variables, it is impossible to know what will happen and we should give up trying.

2. We're not 100% sure a simul-climbing fall will be safe and work in the way some think it will, so you should always just climb unroped instead.

Yes, it's complicated. No, I don't understand the physics. And even physicists may disagree on what would happen here. But the bottom line is that one of these guys is alive because they were tied together, so the system "worked" in my view. I'd prefer to get fucked up in a bad simul-climbing fall caused by my partner falling then watch him careen down a wall because we thought it safer to climb unroped. It's all situational, but this particularly incident has not made me any less likely to choose simulclimbing as a viable option in the mountains.

Time to wrap up and move on. Chief, I'll make one last attempt to explain why mconnell got the right answer and gave the right reason. I'm making this non-insignificant effort for you. Please, read carefully.

We'll start from the ideal case and then, once we understand that, we'll move on to include the "real world disturbances" that trouble you so much.

We need two important laws of Physics:

1. Newton's second law of motion says that the acceleration of a body is proportional to the force applied to it. If you want to stop a falling body in a short distance, you need to apply a large force. If you want to go from 0 to 60 in 5 seconds in a big truck you need more torque than in a bike.

2. Hooke's law of elasticity says that the force exerted by a spring is proportional to its stretch. This proportionality law applies to ideal springs, but we'll see that we can use it for non-ideal real ropes too. The reason is that we only need to assume that the force grows with stretch, not that it is exactly proportional, and that is true of real ropes for not too large stretches, which is all we need. The other important observation is that a long rope is a weaker spring than a short rope. Any climber is aware of that.

Our ideal case has no friction and two identical climbers taking completely clean falls at the same non-zero speed. There is only one piece of pro. There is no slack in the rope and the mass of the rope is negligible compared to the mass of the climbers. We ignore air drag and make other reasonable assumptions of that nature. Once again, we review the ideal case because it provides a baseline for the analysis of real falls.

As the climbers fall, the rope goes through the biner connected to the only piece of pro until the leader hits the biner. At this point both climbers start decelerating. Why? Because the rope is "caught" in the biner and opposes their fall. The rope stretches and in so doing applies a force to the climbers.

Suppose for a moment that the rope were locked off at the biner as soon as the leader reaches it. Then, effectively, the leader and the follower would be falling on two separate ropes: one very long, and the other very short. The long rope would give the follower a very soft catch, but the very short rope would produce forces so high that something would probably break.

However, the rope is not magically locked off at the biner. Therefore, in the absence of friction, it stretches uniformly. This means that its tension is uniform, which means that the two identical climbers are decelerated at the same rate. Since their initial speeds are equal, they remain equal. This can only be achieved by rope moving through the biner from the second's side to the first's side, because initially there is no rope of the leader's side.

All right, we made it through the ideal case. We didn't write any equations. Rather, we did a little bit of what in some circles is called Qualitative Physics. We concluded that in the ideal case, the leader is not stopped abruptly, but decelerates at the same rate as the follower. The middle point of the rope does not move. Each half of the rope arrests one climber. Since the rope that arrests the leader is half the rope between the leader and the second, it is as if the fall factor had been doubled. On the other hand, if the leader had fallen from 10 feet above the last pro in pitched climbing, the rope would have come taut after a 20 feet fall, whereas here it comes taut after just 10 feet because the second is "taking in slack."

Let's not get caught in these details, though, because we still have our main task to undertake.

Let us first assume that everything is like before, but there is friction between rope and biner. The effect of friction is that the tension in the rope is no longer the same on the two sides of the biner. However, it cannot be arbitrarily different. Friction can only do so much. Initially, friction is strong enough to prevent slippage of the rope, but as the very strong spring on the leader's side tries to stop him/her in a very short distance, its tension grows very quickly, which creates a large imbalance until the rope slips.

Something must be noted here. We have not made precise assumptions about the forces. Once again, we have resorted to a qualitative argument. The reason why this works is that the rope on the leader's side is initially so short (in fact, we are assuming zero length) that if no rope slipped through the biner, the imbalance would grow enough to exceed friction. Friction is a complex phenomenon, but once again, we don't need the exact value of the friction force.

We have taken care of friction at the top anchor. Let us now look at weight imbalance between the two climbers. With little or no friction at the biner, we know that eventually the heavier climber will pull up the lighter climber all the way to the biner. Suppose the follower is heavier. Does that prevent the lighter leader from falling lower than the biner? No, because the tension on the follower side is now higher, but the tension on the leader side will grow indefinitely unless there is some slippage. Once it has grown large enough, slippage will occur. Eventually, the leader will bounce up, but that's not our current concern.

We account for more than one piece of pro in the same way. Additional pro adds friction. Friction makes it harder for the leader to pull rope to his/her side. However, if no rope slips, tension grows indefinitely. Hence, at some point, some rope will slip. Less rope than in the absence of friction, but still some.

Once we understand the basic argument, we see how to apply it to other factors. For instance, do we need to assume that the two climbers have the same initial speed? Of course not. Hence, the fact that they didn't have clean falls does not trouble us (though it's likely to trouble them).

Did we ever concern ourselves with the specs of the rope (diameter, impact force rating,...)? No, because from the beginning we stipulated to work only with a qualitative version of Hooke's law that makes no distinction between a Mammut Tusk and a Beal Stinger. In sum, our conclusion for the ideal case continues to hold in the real world.

brenta wrote:"Did we ever concern ourselves with the specs of the rope (diameter, impact force rating,...)? No, because from the beginning we stipulated to work only with a qualitative version of Hooke's law that makes no distinction between a Mammut Tusk and a Beal Stinger. In sum, our conclusion for the ideal case continues to hold in the real world."

There most certainly is distinction between 8.5 Doubles and an 11mm Single especially in the clipping of placed pro within the two distinctive rope techniques and if the pro blows on either system.

I am not concerned with impact force ratings here. Rather, I am concerned with elongation % between the two at 1st drop as both different systems certainly have a clear distinction between the two in a real world fall scenario. Especially if the first piece below the leader blows and there is slack in the the 2nd Double line or twice the amount of drag etc.

Whole different enchilada Brenta. And you would certainly know that had you ever taken substantially lengthy (25+ feet) falls on both systems. Because one will exert a greater initial force on the follower than the other due to their elongation % properties or lack there of.

This is a solid reason Aid (Simul or Belayed) Climbers will never use a Double Rope system.

Diameter of Rope & Rope Type used has much to do with Hooke's Law in this exact scenario and the initial load exerted on the follower.

And how bout them "Twins" for a 25-50 footer..... not!

Your original proposed question was regarding the leader getting sucked up into the first biner after the follower falls. And I say that if a large margin of weight exists between the two with the leader being heavier, the leader will have far less chances of this occurring if they are in fact heavier than the lighter falling follower."The question is: When the leader is pulled into the top biner by the falling follower, does (s)he stop right there, or does the rope start moving through the biner?"

Now, unless you do not take lengthy falls on a regular basis, I do not expect anyone here to even begin to understand this reality.

brenta wrote:"Once we understand the basic argument, we see how to apply it to other factors. For instance, do we need to assume that the two climbers have the same initial speed? Of course not. Hence, the fact that they didn't have clean falls does not trouble us (though it's likely to trouble them)."

Odd, as leader speed increase (distance) or decreases, you are saying that it doesn't play a major factor in the initial Impact Forces on both the elongation properties of the rope and the initial force exerted on the follower? Nor the distance of rope out between climbers either?

The conclusion I came to continues to hold even if we contrast a Tusk and an Ice Line. Your bringing up the single vs. double issue shows that you didn't understand what I wrote at all. Same with the comment about the "large margin of weight."

The Chief wrote:Odd, as leader speed increase (distance) or decreases, you are saying that it doesn't play a major factor in the initial Impact Forces on both the elongation properties of the rope and the initial force exerted on the follower? Nor the distance of rope out between climbers either?

I have said none of that. If you think I did, you should really work on your reading comprehension. Take it easy, one sentence at a time, figure out what it means--which is not whatever hogwash you'd like me to say so that you could prove it wrong--until the big picture emerges.

You are on your own, though. I said it was my last attempt. I'm done with this thread.

brenta wrote:Take it easy, one sentence at a time, figure out what it means--which is not whatever hogwash you'd like me to say so that you could prove it wrong--until the big picture emerges.

I have Fabio and I aint trying to prove you wrong nor potentially deflate your intellectual PhD ego. Get over that.

Basic laws etc do apply in climbing but rest assured that they are not always consistent. Your thesis on paper does not always correlate exactly with real world falling scenarios while climbing, regardless if it's during a simul or belayed scenario. But then one would not understand that if they do not climb in situ's where one takes and personally experiences any kind of lengthy falls on a regular basis. Get out there, push your personal envelope, take some hefty screamers and find out for yourself.

Completely different world than your formula and basic Law/Principal based one. Kind of reminds me of Apollo 13 where those three courageous dudes countered the engineers back in Houston Control then broke every Law and Principal in the book to get their asses back to earth, alive.

Adios Fabio. Good conversation on theory and reality. Out the door to work on another project and probably will take a couple of whippers in the process.

The Chief wrote:I have Fabio and I aint trying to prove you wrong nor potentially deflate your intellectual PhD ego. Get over that.

No worries. It's just frustration at our inability to communicate. Here's how I see our conversation:

F: Two plus two equals four.R: You haven't taken enough whippers to say that.F: Whippers or no whippers, two plus two equals four.R: No, two times two equals four.F: Two plus two equals four too.R: How can you say that two plus two equals forty two?F: Two plus two equals four.R: Two plus two equals four, but not consistently; otherwise those Apollo 13 dudes wouldn't have made it home alive.

At some point, we've got to stop.

The Chief wrote:Out the door to work on another project and probably will take a couple of whippers in the process.

:p Good effort brenta (the long post above). If the team around the Apollo 13 "dudes" hadn't made their homework in "theoretic" sciences first, those dudes wouldn't even have made it off the ground in the first place. But hey trying something out one way first and figuring out why it didn't work later on might work just as fine as the other way around. As for this case, any volunteers? Chief?

FortMental wrote:As a first approximation of a non-dynamic fall, we should take Chief and tie him into 1,000 feet of quadruple static line. Then, anchor him to a dynamometer, the top of the Leaning Tower, push him off, then see if those "basic laws" are consistent with theory.

After that, we should take both halves of his body, put them in a burlap potato sack, and tie him into 300 feet of rubber bands (the kind they use to roll newspapers in) and drop him again as a 1st approximation of a purely dynamic system. Of course, we'll have to test and re-test a few dozen times till we get the sack to gently slow to a stop 1/4 inch from the ground....

Now.... I know this wouldn't be a real world scenario, but it would put end-member constraints on the forces expected when we drop a load of crap in a static vs. dynamic condition.

Why should anyone including myself, even waste their time attempting such a feat as this?

Your post convincingly exhibits the end results of such an endeavor. It is obvious that you landed on your ass and your spine was instantly shoved up into the Brain Stem on impact. Either that, or your mommy had to have dropped you on your head several times during your first year on this planet cus you are definitely one fine specimen of one who is mentally challenged, Formental, clearly evidenced by your consistently inferior intellect posts. It is either the two above theories or you are in fact eating far too much Powerbait thinking it is caviar. Now them are some undisputed real world facts.

Besides, what are you even doing on this thread anyhow, you don't even climb.